https://www.gardeningknowhow.com/houseplants/lipstick-plant/pruning-lipstick-plant.htm

Well, normally...

In this case? I'd cut off any dead ends, absolutely. Those aren't doing any good, but there don't seem to be many; the tips are living.

You can propagate the plant pretty easily by cutting any stems you want, dipping them in rooting hormone, and replanting them in the base plant. Water the plant first so you don't have to for a while.

Others say they do well without the rooting hormone. I never root without it, even just as a safety measure, but also can't say I remember trying to do it with lipstick plant.

Alternately, they can be rooted in a water glass, then planted after they root (no rooting hormone is required for this).

If you want my (rather extreme) opinion here?

I'd take cuttings from the parent plant, it looks like you can get at least six. Then leave the two or three sprigs that remain that are fairly short, and cut away the rest of the plant, essentially restarting it from three or four short strands and the new cuttings, rooted in water. And I'd probably take the opportunity to repot the whole thing in new soil if you haven't in a while.

You'd get the opportunity to reshape the whole new plant the way you want.

But there's room for a whole lot of other things done, as well, depending on what you want to do. It's your plant. You could just take two or three cuttings and regenerate the rest, it'll be just fine. The lowest strands are still living and will probably be perfectly happy to regrow in increasing light in spring.